Calculate the mle estimate for mean, Applied Statistics

Assignment Help:

Each section of the SAT test is supposed to be distributed normally with a mean of 500 and a standard deviation of 100. Suppose 5 students in a class took the SAT math test. They received the following scores: 400, 450, 575, 600, and 625.

(a) Assuming a normal distribution, write out the likelihood function for estimating the mean μ and standard deviation σ of the average class score.

(b) Calculate the MLE estimate for μ and the standard deviation (σ) for this class.

(c) What is the value of the log-likelihood function at this estimate?

(d) What is the least-squares estimate for μ and σ in your data? Are there any differences? Why or why not?

(e) Using a likelihood-ratio test, test whether the MLE estimates from the class are significantly different from the national mean of 500 and national standard deviation of 100.

(Hint: Start by plugging those values into your log-likelihood function. Remember you are testing two restrictions).


Related Discussions:- Calculate the mle estimate for mean

Carpal tunnel statistics, Cindy, the Assistant Vice President of Engineerin...

Cindy, the Assistant Vice President of Engineering/Administrative Services at Blue Cross Blue Shield Rhode Island (BCBSRI), has seen all of the OSHA statistics: In 2000, 1

Good measure of quality, Education seems to be a very difficult field in wh...

Education seems to be a very difficult field in which to use quality methods. One possible outcome measures for colleges is the graduation rate (the percentage of the students matr

Correlation coefficients, What type of correlation coefficient would you us...

What type of correlation coefficient would you use to examine the relationship between the following variables? Explain why you have selected the correlation coefficients. A. Re

Distrbution., The score distribution shown in the table is for all students...

The score distribution shown in the table is for all students who took a yearly AP statistical exam. An AP statistics teacher had 59 students preparing to take the AP exam. Though

Package design ratings, Consider the sample of 60 package design ratings gi...

Consider the sample of 60 package design ratings given in the table below.                                    A Sample of Package Design Ratings                 (Composite S

Cartogram or mapograph, Cartogram or Mapograph:   Statistical maps are a...

Cartogram or Mapograph:   Statistical maps are also used to represent data like density of population indifferent states in the country or different countries in the world or th

Good average, Examine properties of good average with reference to AM, GM, ...

Examine properties of good average with reference to AM, GM, HM, MEAN MEDIAN MODE

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd